Question

Rationalize the denominator of

Answer 1

@ kirbykirby can you see this

Answer 2

A: \[\frac{ -36 + 30i }{ -11 }\]
B: \[\frac{ -3 + 15i }{ 13 }\]
C: \[\frac{ 3 + 15i }{ 13 }\]
D: \[\frac{ 36 + 30i }{ 41 } \]

Answer 3

@kirbykirby

Answer 4

What you can do is in the denominator, simplify that complex addition to one complex number. Then, multiply the top and bottom of the fraction by the conjugate.

Answer 5

so simplify the denominator = 5-1?

Answer 6

i mean 5-i

Answer 7

yes

Answer 8

then conjugate which is 5+i?

Answer 9

\[5 - i(\sqrt{-36} \] ??
is that what im supposed to do next or is that wrong

Answer 10

\[ \frac{\sqrt{-36}}{5-i}=\frac{\sqrt{-36}}{5-i}\cdot \frac{(5+i)}{(5+i)}\]

Answer 11

you can also simplify the numerator, like the \(\sqrt{-36}\) quickly

Answer 12

\[\sqrt{36} = 6 \]
\[6(5 + i)\]
\[\frac{ 30 + 6i }{ ? }\]

Answer 13

is that right so far?

Answer 14

um, \(\sqrt{-36}=\sqrt{(-1)(36)}=\sqrt{-1}\sqrt{36}\)

Answer 15

lol, i just did the square root .-.

Answer 16

so \[\sqrt{-1}\sqrt{36}(5+i) ?\]

Answer 17

-6 + 30i ?

this stuff is confusing to me

Answer 18

@kirbykirby

Answer 19

yes that's good for the numerator (sorry I was answering someone else too :S )

Answer 20

ok so (5-i)(5+i)
but i don't know how to do that?

Answer 21

25 something :P?

Answer 22

method 1: distribute this like as you would do with real polynomials.. like (x-a)(x+a)

method 2: notice this is a difference of squares \(a^2-b^2=(a+b)(a-b)\)

Answer 23

i still don't get how you do it ._.

Answer 24

\[\frac{ -6 + 30i }{ (5+i)(5-i) }\]

Answer 25

\((5+i)(5-i)\)=\(5(5)+5(-i)+i(5)+i(-i)\)=\(25-5i+5i-i^2=25-i^2\)

but \(i^2=-1\)

so:
\(25-i^2=25-(-1)=25+1=26\)

Answer 26

sorry was feeding dogs
so \[\frac{ -6 + 30i }{ 26 } \]
then simplify?
\[\frac{ -3 + 15}{ 13 } \]

Answer 27

yes :) (15i)

Answer 28

Yep oops. They were all right, thank you so much for all the help!!

Answer 29

no problem! :)